For a craft project four students each chose Ihrec Which student chase pieces that can be used to pieces of wire from box. construct a triangle? Don’s wires measure 3 inches. 5 inches, and 12 incles, Don Margo’s wires measure 6 inches, 8 inches, and 14 Margo inches. Sonj’s wires measure 12 inches, 8 inches, and 17 Sonji inches. Liam Liam’s wires measure 16 inches, 8 inches, and 27 inches. uk_this and recurn
The Correct Answer and Explanation is :
To determine which student’s wires can be used to form a triangle, we need to apply the Triangle Inequality Theorem. The theorem states that for three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, for three sides ( a ), ( b ), and ( c ), the following inequalities must hold:
- ( a + b > c )
- ( a + c > b )
- ( b + c > a )
Now, let’s check each student’s wire lengths:
Don’s wires: 3 inches, 5 inches, 12 inches
- ( 3 + 5 = 8 ) (which is less than 12)
- This doesn’t satisfy the Triangle Inequality Theorem. Therefore, Don’s wires cannot form a triangle.
Margo’s wires: 6 inches, 8 inches, 14 inches
- ( 6 + 8 = 14 ) (which is equal to 14, not greater)
- This doesn’t satisfy the Triangle Inequality Theorem. Therefore, Margo’s wires cannot form a triangle.
Sonji’s wires: 12 inches, 8 inches, 17 inches
- ( 12 + 8 = 20 ) (which is greater than 17)
- ( 12 + 17 = 29 ) (which is greater than 8)
- ( 8 + 17 = 25 ) (which is greater than 12)
- All inequalities are satisfied. Therefore, Sonji’s wires can form a triangle.
Liam’s wires: 16 inches, 8 inches, 27 inches
- ( 16 + 8 = 24 ) (which is less than 27)
- This doesn’t satisfy the Triangle Inequality Theorem. Therefore, Liam’s wires cannot form a triangle.
Conclusion:
- Only Sonji‘s wires (12 inches, 8 inches, and 17 inches) satisfy the Triangle Inequality Theorem and can be used to construct a triangle.
Let me generate the image that visually shows this concept.
Here is the visual representation showing which sets of wire lengths can and cannot form a triangle based on the Triangle Inequality Theorem. As you can see, only Sonji’s wires (12 inches, 8 inches, and 17 inches) can form a triangle, while the other sets cannot.